**[2 marks]**Let . Evaluate . In other words, find the derivative of at .

(a) (b) (c) (d)

**[2 marks]**Let . Evaluate . In other words, find the second derivative of at .

(a) (b) (c) (d)

**[2 marks]**Let . Calculate

**[2 marks]**Evaluate the following limit: .

(a) (b) (c) (d)

**[2 marks]**A differentiable function has the property that , and . What is the value of the derivative of at ?

(a) (b) (c) (d)

**[2 marks]**Let . Evaluate . In other words, find the derivative of at .

(a) (b) (c) (d)

**[2 marks]**Let y be given implicitly as a differentiable function of by . Then the slope of the tangent line to the curve at the point where , is equal to:

(a) , (b) , (c) , (d) .

**[2 marks]**Let . Evaluate . In other words, find the derivative of at .

(a) (b) (c) (d)

**[2 marks]**Let . Calculate in the case where is a point where .

(a) (b) (c) (d) None of these

**[2 marks]**Evaluate using any method.

(a) (b) (c) (d)

**[2 marks]**Evaluate

(a)

(b)

(c) This limit does not exist (d)

**[2 marks]**Which of the following functions represents the form of the inverse function of the function whose domain is the set of all real numbers where .

(a) where

(b) where

(c) where

(d)

**[2 marks]**Solve the inequality for .

(a)

(b)

(c)

(d)

- Determine an interval where the graph of the function defined by the polynomial
is concave up.

(a)

(b)

(c)

(d)

**[2 marks]**Which of the following functions has a point of inflection at ?

(a)

(b)

(c)

(d)

**[2 marks]**For what values of is the function increasing?

(a)

(b)

(c)

(d)

**[2 marks]**Find all the critical points of

(a)

(b)

(c)

(d)

**[2 marks]**An antiderivative of is given by

(a)

(b)

(c)

(d)

**[2 marks]**Evaluate

(a)

(b)

(c)

(d)

**[2 marks]**Evaluate

(a)

(b)

(c)

(d)

**[2 marks]**The value of is

(a)

(b)

(c)

(d)

**[2 marks]**The most general antiderivative of is given by

(a)

(b)

(c)

(d)

**[2 marks]**Evaluate and simplify the indefinite integral: .

(a)

(b)

(c)

(d)

**[2 marks]**Evaluate the improper integral .

(a)

(b)

(c)

(d)

**[2 marks]**The form of the partial fraction decomposition of the rational function

(a)

(b)

(c)

(d)

where are constants to be determined.

**[2 marks]**Evaluate the indefinite trigonometric integral

(a)

(b)

(c)

(d)

where are constants to be determined.

**[2 marks]**The area enclosed by the intersection of the two curves defined by and is given by which of the following definite integrals?

(a)

(b)

(c)

(d)

**[2 marks]**Which of the following expressions gives the**volume**of the solid of revolution obtained when the region bounded by the graphs of and is revolved about the**axis**?

(a)

(b)

(c)

(d)

**[2 marks]**The center of mass of a thin quarter circle of radius having uniform density and situated in the first quadrant is given by which of the following points?

(a)

(b)

(c)

(d)

**[2 marks]**The general solution of the differential equation

(a)

(b)

(c) (d)